B · Notation - Robots That Perceive

This table grows as chapters are added.

Symbol	Meaning	First used
$x_t$	state at time $t$	1.1
$z_t$	measurement at time $t$	1.1
$u_t$	action or control input	1.1
$z_{1:t}$	all measurements from time 1 to $t$	1.1
$\pi$	policy: the robot’s decision rule	1.1
$f,\ h$	motion model, measurement model	1.2
$w_t,\ v_t$	process noise, measurement noise	1.2
$T_{ij}$	transition probability from state $i$ to state $j$	1.2
$(p_x, p_y, \theta)$	planar position and heading	1.2
$v,\ \omega$	forward speed, turn rate	1.2
$P(\cdot)$ , $p(\cdot)$	probability (discrete), density (continuous)	2.1
$\mathcal{N}(x;\mu,\sigma^2)$	Gaussian density	2.1
$\mu,\ \sigma^2$	mean, variance	2.1
$C(a,x)$	cost of action $a$ when the state is $x$	2.4

Estimates carry a hat ( $\hat{x}$ ).